Problem: What do the following two equations represent? $-2x+3y = 2$ $10x-15y = 3$
Putting the first equation in $y = mx + b$ form gives: $-2x+3y = 2$ $3y = 2x+2$ $y = \dfrac{2}{3}x + \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $10x-15y = 3$ $-15y = -10x+3$ $y = \dfrac{2}{3}x - \dfrac{1}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.